Distributed Point Functions and Function Secret Sharing

2026-07-30

AI Summary

This work investigates efficient constructions for compressive additive secret sharing of point functions among multiple parties and extends this approach to broader function classes to support diverse secure computation applications. By generalizing distributed point functions (DPFs) from single-point functions to generic function secret sharing (FSS) schemes, the study proposes lightweight and highly efficient protocols that substantially broaden the applicability of DPFs in privacy-preserving computation. The paper systematically reviews the theoretical foundations and core techniques underlying DPFs and FSS, and advances their practical deployment in real-world scenarios such as private information retrieval, anonymous communication, and secure multi-party computation, thereby enhancing both the security and practicality of the preprocessing phase.

Abstract

A distributed point function (DPF) is a cryptographic primitive that enables compressed additive sharing of a secret weight-1 vector (equivalently, a point function) across two or more parties. The appealing lightweight structure of DPF constructions has enabled a wide range of applications. These include private information retrieval, anonymous messaging, secure computation with preprocessing, and pseudorandom correlation generators for expanding small correlated seeds into large pseudorandom instances of cryptographic correlations. In this article, we survey definitions, constructions, and applications of DPFs. We also discuss the extension of DPF to function secret sharing (FSS), which generalizes point functions to support richer function classes. Efficient FSS schemes yield a similar generalization for most of the applications of DPFs.

Problem

• Distributed Point Functions
• Function Secret Sharing
• Secret Sharing
• Point Functions
• Cryptographic Primitives

Innovation

• Distributed Point Functions
• Function Secret Sharing
• Additive Secret Sharing
• Pseudorandom Correlation Generators
• Secure Computation